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Yemen's former president Ali Abdullah Saleh should be killed "be killed and hanged at the Gate of Yemen," the country's Houthi rebels said on Friday, in the latest rift between the allies.

Saleh, who along with the Houthis, has jointly controlled the capital Sana'a since September 2014, was accused of treason by the rebel group and has faced a tirade of verbal attacks across rebel-owned platforms, including al-Masirah television channel and SamFM radio.

But the comments are just the latest in tension between the two camps in recent weeks, after a fresh wave of mutual accusations which threaten their three-year alliance.

On Thursday, Saleh's General People's Congress (GPC) complained of humiliation at the hands of the Houthis, accusing the rebels of waging an "orchestrated campaign" against the former strongman.

The GPC said in an open letter to Ansar Allah, the political party led by Houthi chief Abdulmalik al-Houthi, that its ministers had been "humiliated" by the rebels who "lack the will to maintain partnership".

Ansar Allah in turn accused the GPC of breaking their pact with the Houthis and accepting money from the rival government of President Abedrabbo Mansour Hadi, a statement said.

The party's political leader Salah Sammad accused the GPC of "sapping internal unity" and paralysing the rebel government.

Tensions between Yemen's Houthi rebels and their ally Saleh reached boiling point in August after the Houthis accused the former president of treason after he dismissed the Iranian-backed rebels as "militias".

Saleh as president had fought successive wars against the Houthis but they joined ranks in 2014 to drive the Hadi government out of Sana'a.

The war between the government of President Abd Rabbo Mansour Hadi, backed by the coalition, and the rebel camp has killed more than 10,000 Yemenis since 2015 and pushed the country to the brink of famine.